Transition from band insulator to Mott insulator in one dimension:  Critical behavior and phase diagram

We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U=U_c and U=U_s that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<U_c) and drops below the band gap when U exceeds a special point U_e. The exciton gap closes at the first critical point U_c while the charge and spin gaps persist and coincide between U_c<U<U_s where the system is dimerized. Both the charge and spin gaps collapse at U=U_s when the transition to the MI phase occurs. In the MI phase (U>U_s) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.